(Symplectic) Leaves and (5d Higgs) Branches in the Poly(go)nesian Tropical Rain Forest

Understand

We derive the structure of the Higgs branch of 5d superconformal field theories or gauge theories from their realization as a generalized toric polygon (or dot diagram).

• This approach is motivated by a dual, tropical curve decomposition of the $(p,q)$ 5-brane-web system.
• We define an edge coloring, which provides a decomposition of the generalized toric polygon into a refined Minkowski sum of sub-polygons, from which we compute the magnetic quiver.
• The Coulomb branch of the magnetic quiver is then conjecturally identified with the 5d Higgs branch.